Hypersatisfaction of formulas in agebraic systems

• Autorzy: Klaus Denecke , Dara Phusanga
• Języki publikacji: EN

Abstrakty

EN

In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an ordered algebra.

Słowa kluczowe

EN

algebraic system; formula; relational clone; hyperformula

Kategorie tematyczne

• 03B50: Many-valued logic
• 08A30: Subalgebras, congruence relations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 123-151

Daty

wydano

2009

otrzymano

2009-05-15

poprawiono

2009-11-03

Twórcy

autor

Klaus Denecke

• Universität Potsdam Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam (Germany)

autor

Dara Phusanga

• Universität Potsdam Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam (Germany)

Bibliografia

• [1] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers 2000.
• [2] K. Denecke and D. Phusanga, Hyperformulas and Solid Algebraic Systems, Studia Logica 90 (2) (2008) 263-286.
• [3] E. Graczyńska and D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990) 305-318.
• [4] J. Koppitz and K. Denecke, M-solid Varieties, Springer 2006.
• [5] A.I. Mal'cev, Algebraic Systems, Akademie-Verlag, Berlin 1973.
• [6] R. Pöschel and L.A. Kalužnin, Funktionen-und Relationenalgebren, VEB Deutscher Verlag der Wissenschaften, Berlin 1979.
• [7] J.A. Goguen and R.M. Burstall, Introducing Institution, in Proceeding of the Logic of Programming Workshop (1984) 221-256.
• [8] J.A. Goguen and R.M. Burstall, Institutions: Abstract Model Theory for Specification and Programming, Journal of the ACM 39 (1) (1992) 95-146.

Identyfikatory

DOI

10.7151/dmgaa.1154